There is a beam 60 cm long, which is supported at a distance of 40 cm from the left end, where a force of 20

There is a beam 60 cm long, which is supported at a distance of 40 cm from the left end, where a force of 20 N is applied downward. At a distance of 10 cm from the support on the right, a force of 40 N is applied upward. What force, directed downward, must be applied to the right end of the rod to was he in balance?

Given:

L = 60 centimeters = 0.6 meters – the total length of the beam;

l1 = 40 centimeters = 0.4 meters – the point of support of the beam from the left end;

F1 = 20 Newton – force applied to the left end of the beam (downward);

l2 = 10 centimeters = 0.1 meter – the distance from the fulcrum (right) to the point of application of the force F2;

F2 = 40 Newton – the force applied to the point l2 (up).

It is required to determine F3 (Newton) – what force must be applied to the right end of the support so that the support is in balance.

Since the condition of the problem is not specified, we do not take into account the mass of the beam in solving the problem.

Find the distance from the pivot point to the right end of the beam:

l3 = L – l1 = 0.6 – 0.4 = 0.2 meters.

Then, taking into account the direction of forces (downward – positive, upward – negative), we get:

F1 * l1 = -F2 * l2 + F3 * l3;

F1 * l1 + F2 * l2 = F3 * l3;

F3 = (F1 * l1 + F2 * l2) / l3 = (40 * 0.4 + 20 * 0.1) / 0.2 =

= (16 + 2) / 0.2 = 18 / 0.2 = 90 Newtons.

Answer: it is necessary to apply a force equal to 90 Newtons.